Question: Solve for $x$ and $y$ using elimination. ${2x+3y = 18}$ ${-2x+2y = 2}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $5y = 20$ $\dfrac{5y}{{5}} = \dfrac{20}{{5}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x+3y = 18}\thinspace$ to find $x$ ${2x + 3}{(4)}{= 18}$ $2x+12 = 18$ $2x+12{-12} = 18{-12}$ $2x = 6$ $\dfrac{2x}{{2}} = \dfrac{6}{{2}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {-2x+2y = 2}\thinspace$ and get the same answer for $x$ : ${-2x + 2}{(4)}{= 2}$ ${x = 3}$